Efficiency of Carnot's Engine.
H being the effective work given to the engine. Reckoning the
heat used, we have :
From i to 2 (r^). Heat expended, being work area i,
= P1V1 loge *i = ^ loge rv
From 2 to 3 (r%). No heat expended, external work, j, being
done by abstraction of heat from the gas.
From 3 to 4 (r^). Heat rejected, as at K,
From 4 to i (r^). No heat rejected, external work, at L, pro-
ducing internal work on the gas.
We have previously found (p. 607) the comparison of tempera-
ture in terms of r, during adiabatic expansion or compression :
from which may be deduced:
Referring to Fig. 617, expansion from 2 to 3 and compression
from 4 to i are between the same temperatures, so the ratio of
adiabatic expansion equals that of adiabatic compression : r2 = r±
And as, ~3 - ™4
i »») »q
and — = -
vl , vl
Or the ratio of isothermal expansion equals that of isothermal
compression: r^ = r^ = r, say.
Resuming; when the cycle is complete no internal work has
been done—all is external work:
. . External work = Heat expended - Heat rejected
= CT lOe ^ - *r lOge > - (T ~ T C
Efficiency of Engine :
--------17ET75-------"^ & &' 7<58' 883' 887'
i v. &« / ------1— 934, and 966.)
It will be easily seen that for the highest efficiency, r2 must be
nothing, or the condenser must have a temperature of * absolute